With MSA it says "Windows is activated with a digital license linked to your Microsoft account". Change to local and it just drops the words "linked to your Microsoft account". Change back and they come back again.
My understanding is linking to MSA helps with moving you license that is all (as you said).
I actually just did a clean install (using a local account) after being activated using a MSA and it activated fine so I'm pretty sure changing to local account doesn't mean you lose your license.
Perhaps the original machine would lose the license if you transferred it to a new machine but I don't know as I've not tried that.